Two coins are tossed- What is the conditional probability that two heads result- given that there is least one -displaystyle frac-2-3-displaystyle frac-1-3-displaystyle frac-3-4-displaystyle frac-1-4-

Question

Toppr Admin · Accepted Answer

Let A be the event that two heads result and B the event that there is at least one head.
If S denote the sample space, then $S = {(H, H), (H, T) (T, H) (T, T)}$
$A = {(H, H)}$
$B = {(H, H), (H, T) (T, H)}$
So, $A \cap B = {H, H}$
$P (B) = \frac{3}{4},$
$P (A \cap B) = \frac{1}{4}$
Hence $P (A | B) = \frac{P (A \cap B)}{P (B)}$
$= \frac{1 / 4}{3 / 4} = \frac{1}{3}$

Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?23133414

Let A be the event that two heads result and B the event that there is at least one head.If S denote the sample space, then S={(H,H),(H,T)(T,H)(T,T)} A={(H,H)} B={(H,H),(H,T)(T,H)} So, A∩B={H,H}P(B)=34, P(A∩B)=14 Hence P(A|B)=P(A∩B)P(B)=1/43/4=13

Two coins are tossed. What is the conditional probability that two heads result, given that there is at least one head ?
$\frac{2}{3}$
$\frac{1}{3}$
$\frac{3}{4}$
$\frac{1}{4}$