Question

$A$ and $B$ toss a fair coin each simultaneously $50$ times.The probability that both of them will not get tail at the same toss is

• A. $(3/4{)}^{50}$
• B. $(2/7{)}^{50}$
• C. $(1/8{)}^{50}$
• D. $(7/8{)}^{50}$

Answer 1

The correct option is A $(3/4{)}^{50}$

At any trial, four cases arise

(i) both A and B get head

(ii) A gets head, B gets tail

(iii) A gets tail, B gets head

(iv) both get tail

$⟹$ P(they do not get tail simultaneously on a particular trail = $\frac{3}{4}$

$⟹$ P(they do not get tail simultaneously in 50 trials) =${\left(\frac{3}{4}\right)}^{50}$