If P and Q each toss three coins. The probability that both gets same number of heads, is

Question

If P and Q each toss three coins. The probability that both gets same number of heads, is (A) (3/8) (B) (1/9) (C) (3/16) (D) (5/16)

Tardigrade Admin · Accepted Answer

Let p and q represents the probability of getting head and tail respectively on tossing a coin. So, p=q=(1/2) So, required probability = displaystyle∑r=03[ 3 C,((1/2))3]2 =((1/2))6[12+32+32+12] =(20/64)=(5/16)

Q. If $P$ and $Q$ each toss three coins. The probability that both gets same number of heads, is

$\frac{3}{8}$

$\frac{1}{9}$

$\frac{3}{16}$

$\frac{5}{16}$

Let $p$ and $q$ represents the probability of getting head and tail respectively on tossing a coin.
So, $p = q = \frac{1}{2}$
So, required probability $= r = 0 \sum 3 [^{3} C_{,} (\frac{1}{2})^{3}]^{2}$
$= (\frac{1}{2})^{6} [1^{2} + 3^{2} + 3^{2} + 1^{2}]$
$= \frac{20}{64} = \frac{5}{16}$

Q. If P and Q each toss three coins. The probability that both gets same number of heads, is

83​

91​

163​

165​