First slide

Random variable and probability distribution

Question

If A and B each toss three coins. The probability that both get the same number of heads is

Moderate

A

1/9
B

3/16
C

5/16
D

3/8

Solution

The probability that A gets r heads in three tosses of a coin is
$P (X = r) =^{3} C_{r} {(\frac{1}{2})}^{r} {(\frac{1}{2})}^{3 - r} =^{3} C_{r} {(\frac{1}{2})}^{3}$
The probability that A and B both get r heads in three tosses of a coin is
$^{3} C_{r} {(\frac{1}{2})}^{3}^{3} C_{r} {(\frac{1}{2})}^{3} = {(^{3} C_{r})}^{2} {(\frac{1}{2})}^{6}$
Hence, the required probability is
$\sum_{r = 0}^{3} {(^{3} C_{r})}^{2} {(\frac{1}{2})}^{6} = {(\frac{1}{2})}^{6} {1 + 9 + 9 + 1} = \frac{20}{64} = \frac{5}{16}$

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