Independent Events

Given that A and B are not null sets, which of the following statements regarding probability is/are CORRECT?

Given that $A$ and $B$ are not null sets, which of the following statements regarding probability is/are CORRECT?

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decim...

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decim...

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tos...

A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the...

$$X$$ and $$Y$$ are two random independent events. It is known that $$P(X)=0.40$$ and $$\,P\left( {X \cup {Y^C}} \right) = 0.7.$$ Which one of the following is the value of $$P\lef...

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes; (i) Head, (ii) Head, (III) Head, (iv) Head. The probability of obtaining a ''Tail...

There are two containers with one containing $$4$$ red and $$3$$ green balls and the other containing $$3$$ blue balls and $$4$$ green balls. One ball is drawn at random from each...

Two coins are simultaneously tossed. The probability of two heads simultaneously appearing

A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed, the probability that both ga...