A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up. From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Question

Philoid · Accepted Answer

Here the sample space is,

S = (HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, HTTH, THTH, TTHH,

TTTH, TTHT, THTT, HTTT, TTTT)

According to the given condition, a person will win or lose money depending up on the face of the coin so,

(i) For 4 heads = 1 + 1 + 1 + 1 = Rs. 4 = he wins Rs. 4

(ii) For 3 heads and 1 tail = 1 + 1 + 1 – 1.50 = Rs. 1.50 = he will be winning Rs. 1.50

(iii) For 2 heads and 2 tails = 1 + 1 – 1.50 – 1.50 = - Rs. 1 = he will be losing Re. 1

(iv)For 1 head and 3 tails = 1 – 1.50 – 1.50 – 1.50 = - Rs. 3.50 = he will be losing Rs. 3.50

(v) For 4 tails = – 1.50 – 1.50 – 1.50 – 1.50 = - Rs. 6 = he will be losing Rs. 6

Now the sample space of amounts is

S= {4, 1.50, 1.50, 1.50, 1.50, – 1, – 1, – 1, – 1, – 1, – 1, – 3.50, – 3.50, – 3.50, – 3.50, – 6}

∴ n (S) = 16