$A$ person has undertaken a construction job. The probabilities are $0.65$ that there will be a strike,$0.80$ that the construction job will be completed on time if there is no strike,and $0.32$ that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

If two cards are drawn one after the other without replacement from a well-shuffled ordinary deck of $52$ cards, then the probability that both of them are aces is

In a box of $10$ electric bulbs,two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection is put back in the box before making the second selection. The probability that both the bulbs are without defect is

$A$ bag contains $4$ red and $3$ blue balls. Two balls are drawn one after another. If the first ball is replaced before drawing the second,what is the probability that the first ball is red and the second ball is blue?

Three groups $A, B, C$ are competing for positions on the Board of Directors of a company. The probabilities of their winning are $0.5, 0.3, 0.2$ respectively. If group $A$ wins,the probability of introducing a new product is $0.7$,and the corresponding probabilities for groups $B$ and $C$ are $0.6$ and $0.5$ respectively. The probability that the new product will be introduced is:

$A$ woman has $10$ keys,out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) until she succeeds in opening the lock. What is the probability that the seventh key works?