Question 1: List the outcomes you can see in these experiments.
(a) Spinning a wheel.
Solution: Notice that you are given with only 4 options, which are A, B, C and D. Though you have 5 divisions, it would create no difference on the outcomes of spinning whether you get A(the one before B) or the A (the one after D).
There are only 4 outcomes.
(b) Tossing two coins together.
Solution: On a single coin, you may get H(head) or T(tail), but when two are tossed, you may get T on 1st and H on 2nd, T on 1st and T on 2nd as well.
Similarly, you get TH, TT, HT, HH.
You have 4 outcomes.
Question 2: When a die is thrown, list the outcomes of an event of getting
(a) a prime number.
Solution: When a die is thrown, you have 1, 2, 3, 4, 5, and 6 as outcomes.
Out of these, 2, 3, and 5 are prime number.
Hence, outcome should be any one of 2, 3 and 5.
(b) not a prime number.
Solution: All other options, which are not considered as prime, are non-prime numbers.
Therefore, outcomes should be any one of 1, 4 and 6.
(c) a number greater than 5.
Solution: Out of 1, 2, 3, 4, 5, 6, 6 is the only number which is greater than 5.
Hence, outcome should be 6.
(d) a number not greater than 5.
Solution: A number which is not greater than 5 can be 5 itself including 1, 2, 3 and 4.
Hence, outcome should be 1, 2, 3, 4, 5.
Question 3: Find the:
(a) Probability of the pointer stopping on D in question 1(a).
Solution: Pointer has 5 places to stop in total, but there's just one place out of those 5 where pointer can find D ?
So, number of total outcome = 5
number of favorable outcome = 1
Hence, probability = 1/5
*question 1(a) and this have different meaning.
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards ?
Solution: there are only 4 ace cards out of 52 cards.
So, number of total outcome = 52
number of favorable outcome = 4
Hence, probability = 4/52 = 1/13
(c) Probability of getting a red apple(figure given)?
There are 4 red apples and 3 green apples, and in total there are 7 apples
Hence, probability of getting a red apple = 4/7
Question 4: Number 1 to 10 are written on ten separate slips(one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of
(i) getting a number 6
Solution: There's only 1 chance that you may get 6, out of all 10.
Hence, favorable outcomes = 1
total outcomes = 10
Probability of getting 6 = 1/10
(ii) getting a number less than 6
Solution: numbers less than 6 are 1, 2, 3, 4 and 5.
favorable outcomes = 5
total outcomes = 10
probability of getting a number less than 6 is 5/10 = 1/2
(iii) getting a number greater than 6
Solution: numbers greater than 6 are 7, 8, 9 and 10.
favorable outcomes = 4
total outcomes = 10
probability of getting a number greater than 6 is 4/10 = 2/5
(iv) getting a 1-digit number
Solution: all the number from 1 to 10 are 1 digit number except 10.
therefore, total outcomes = 10
favorable outcomes = 10 - 1 = 9
probability of getting a 1-digit number = 9/10
Question 5: If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector. What is the probability of getting a green sector ?What is the probability of getting a non-blue sector?
Solution: Total number of sectors = 3 + 1 + 1 = 5
Total number of green sector = 3
Hence, Probability of getting a green sector = 3/5
Total number of non-blue sectors = number of green + red sector = 3 + 1 = 4
Hence, probability of getting a non-blue sector = 4/5
Question 6: Find the probabilities of the event given in Question 2.
Answers & Comments
Answer:
hi... check the below picture
Verified answer
Answer:
Step-by-step explanation:
Question 1: List the outcomes you can see in these experiments.
(a) Spinning a wheel.
Solution: Notice that you are given with only 4 options, which are A, B, C and D. Though you have 5 divisions, it would create no difference on the outcomes of spinning whether you get A(the one before B) or the A (the one after D).
There are only 4 outcomes.
(b) Tossing two coins together.
Solution: On a single coin, you may get H(head) or T(tail), but when two are tossed, you may get T on 1st and H on 2nd, T on 1st and T on 2nd as well.
Similarly, you get TH, TT, HT, HH.
You have 4 outcomes.
Question 2: When a die is thrown, list the outcomes of an event of getting
(a) a prime number.
Solution: When a die is thrown, you have 1, 2, 3, 4, 5, and 6 as outcomes.
Out of these, 2, 3, and 5 are prime number.
Hence, outcome should be any one of 2, 3 and 5.
(b) not a prime number.
Solution: All other options, which are not considered as prime, are non-prime numbers.
Therefore, outcomes should be any one of 1, 4 and 6.
(c) a number greater than 5.
Solution: Out of 1, 2, 3, 4, 5, 6, 6 is the only number which is greater than 5.
Hence, outcome should be 6.
(d) a number not greater than 5.
Solution: A number which is not greater than 5 can be 5 itself including 1, 2, 3 and 4.
Hence, outcome should be 1, 2, 3, 4, 5.
Question 3: Find the:
(a) Probability of the pointer stopping on D in question 1(a).
Solution: Pointer has 5 places to stop in total, but there's just one place out of those 5 where pointer can find D ?
So, number of total outcome = 5
number of favorable outcome = 1
Hence, probability = 1/5
*question 1(a) and this have different meaning.
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards ?
Solution: there are only 4 ace cards out of 52 cards.
So, number of total outcome = 52
number of favorable outcome = 4
Hence, probability = 4/52 = 1/13
(c) Probability of getting a red apple(figure given)?
There are 4 red apples and 3 green apples, and in total there are 7 apples
Hence, probability of getting a red apple = 4/7
Question 4: Number 1 to 10 are written on ten separate slips(one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of
(i) getting a number 6
Solution: There's only 1 chance that you may get 6, out of all 10.
Hence, favorable outcomes = 1
total outcomes = 10
Probability of getting 6 = 1/10
(ii) getting a number less than 6
Solution: numbers less than 6 are 1, 2, 3, 4 and 5.
favorable outcomes = 5
total outcomes = 10
probability of getting a number less than 6 is 5/10 = 1/2
(iii) getting a number greater than 6
Solution: numbers greater than 6 are 7, 8, 9 and 10.
favorable outcomes = 4
total outcomes = 10
probability of getting a number greater than 6 is 4/10 = 2/5
(iv) getting a 1-digit number
Solution: all the number from 1 to 10 are 1 digit number except 10.
therefore, total outcomes = 10
favorable outcomes = 10 - 1 = 9
probability of getting a 1-digit number = 9/10
Question 5: If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector. What is the probability of getting a green sector ?What is the probability of getting a non-blue sector?
Solution: Total number of sectors = 3 + 1 + 1 = 5
Total number of green sector = 3
Hence, Probability of getting a green sector = 3/5
Total number of non-blue sectors = number of green + red sector = 3 + 1 = 4
Hence, probability of getting a non-blue sector = 4/5
Question 6: Find the probabilities of the event given in Question 2.
Solution:
(a): Prime number
Total number of outcomes = 6
Favorable number of outcomes = 3 [2, 3 & 5 ]
required Probability = 3/6 = 1/2
(b): not a prime number
Total number of outcomes = 6
Favorable number of outcomes = 3 [1, 4 & 6 ]
required Probability = 3/6 = 1/2
(c): a number greater than 5
Total number of outcomes = 6
Favorable number of outcomes = 1 [6]
required Probability = 1/6
(d): a number not greater than 5
Total number of outcomes = 6
Favorable number of outcomes = 5 [1, 2, 3, 4, 5 ]
required Probability = 5/6