A player receives 250 pesos if the results of tossing three coins are all heads or all tails on the other hand he or she receives 150 pesos if either one or two heads show. what is the expected gain of the player? what does the result imply?
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Solution:
Total number of trials = 250.
Number of times three heads appeared = 70.
Number of times two heads appeared = 55.
Number of times one head appeared = 75.
Number of times no head appeared = 50.
In a random toss of 3 coins, let E1, E2, E3 and E4 be the events of getting three heads, two heads, one head and 0 head respectively. Then,
(i) getting three heads
P(getting three heads) = P(E1)
Number of times three heads appeared
= Total number of trials
= 70/250
= 0.28
(ii) getting two heads
P(getting two heads) = P(E2)
Number of times two heads appeared
= Total number of trials
= 55/250
= 0.22
(iii) getting one head
P(getting one head) = P(E3)
Number of times one head appeared
= Total number of trials
= 75/250
= 0.30
(iv) getting no head
P(getting no head) = P(E4)
Number of times on head appeared
= Total number of trials
= 50/250
= 0.20
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