One card is drawn at random from a well shuffled deck of $52$ cards. In which of the following cases are the events $\mathrm{E}$ and $\mathrm{F}$ independent ?
$E:$ ' the card drawn is a king and queen '
$F:$ ' the card drawn is a queen or jack '
The probabilities that a student passes in Mathematics, Physics and Chemistry are $m, p$ and $c$ respectively. On these subjects, the student has a $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ chance of passing in exactly two. Which of the following relations are true
Check whether the following probabilities $P(A)$ and $P(B)$ are consistently defined $P ( A )=0.5$, $ P ( B )=0.7$, $P ( A \cap B )=0.6$
A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is
The probability that at least one of $A$ and $B$ occurs is $0.6$. If $A$ and $B$ occur simultaneously with probability $0.3$, then $P(A') + P(B') = $