NCERT Class XI Mathematics - Probability - Solutions

Question : 30

Total: 54

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.

Solution:

An experiment consists of tossing a fair coin four times. Therefore, the sample space of the given experiment is given by
S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THTH, TTHH, THHT, HTTT, THTT, TTHT, TTTH, TTTT}
∴ n(S) = 16
According to question, we have

Event

Favourble outcome (E)

Possible outcome (S)

Probability (

n(E)

n(S)

)

Gain/Loss

(i) No head and 4 tail

{TTTT}
∴ n(E) = 1

n(S) = 16

1/16

Loss = Rs. 4 × 1.50
= Rs.6

(ii) 1 head and 3 tails

{HTTT, THTT, TTHT, TTTH}
∴ n(E) = 4

n(S) = 16

4/16 = 1/4

Loss = Rs (–1 × 1 + 3 × 1.50)
= Rs. 3.50

(iii) 2 heads and 2 tails

{HHTT, HTTH, HTHT, THTH, TTHH, THHT}
∴ n(E) = 6

n(S) = 16

6/16 = 3/8

Loss = Rs. (2 × 1.5 – 2 × 1)
= Rs. 1

(iv) 3 heads and 1 tail

(HHHT, HTHH, HHTH, THHH}
∴ n(E) = 4

n(S) = 16

4/16 = 1/4

Gain = Rs. (3 × 1 – 1 × 1.50)
= Rs. 1.50

(v) All heads

{HHHH}
∴ n(E) = 1

n(S) = 16

1/16

Gain = Rs. (4 × 1)
= Rs. 4

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