List of top Mathematics Questions on Probability asked in UP Board XII

A family has two children. If it is known that at least one child is a boy, then find the probability of both children being boys.

If \(P(A)=\dfrac{7}{13}\), \(P(B)=\dfrac{9}{13}\) and \(P(A\cap B)=\dfrac{4}{13}\), then find \(P(A/B)\).

It is given that the numbers obtained on throwing two dice are different. Find the probability that the sum of both numbers is 4.

Prove that if \(E\) and \(F\) are independent events, then \(E\) and \(F'\) will also be independent.

If \(P(A)=0.8,\ P(B)=0.5\) and \(P(B\mid A)=0.4\), find \(P(A\cup B)\).

If a die is thrown three times, then find the probability of getting at least one odd number.

If \(P(A)=\dfrac13\), \(P(B)=\dfrac12\) and \(P(A\cup B)=\dfrac23\), then show that \(A\) and \(B\) are independent events.

If \(P(A)=\dfrac7{13}\), \(P(B)=\dfrac9{13}\) and \(P(A\cap B)=\dfrac4{13}\), then find \(P\left(\dfrac AB\right)\).

A die is thrown twice and found that the sum of the numbers is 6. Find the conditional probability of getting number 4 at least once.

If \(P(A)=\dfrac12\), \(P(B)=\dfrac13\) and \(A,B\) are independent events, find the value of \(P(A/B)\).

Prove that if \(E\) and \(F\) are two independent events, then \(E\) and \(F'\) will also be independent.

If \(A\) and \(B\) are independent events and \(P(A)=0.3\), \(P(B)=0.4\), then find (i) \(P(A\cap B)\), (ii) \(P(A\cup B)\).

The probability of impossible events is:

Prove that if \(A\) and \(B\) are independent events, then the probability of happening of at least one of \(A\) or \(B\) is \(\left[1-P(A')P(B')\right]\).

If \(P(A)=\dfrac{7}{13}\), \(P(B)=\dfrac{9}{13}\) and \(P(A\cap B)=\dfrac{4}{13}\), then find \(P(A\cup B)\) and \(P(A/B)\).

If \(3P(A)=P(B)=\dfrac{5}{13}\) and \(P(A/B)=\dfrac{2}{5}\), then \(P(A\cup B)\) will be:

If \( P(A) = 0.12, P(B) = 0.15 \) and \( P(B/A) = 0.18 \), then find the value of \( P(A \cap B) \).