Two numbers are randomly selected and multiplied. Consider two events `E_(1)and E_(2)` defined as
`E_(1):` Their product is divisible by 5
`E_(2):` Unit's places in their product is 5
Which of the following statement is/are correct ?

Two whole numbers are randomly selected and multiplied. Consider two events E_1 and E_2 defined as E_1 : Their product is divisible by 5 and E_2 Unit's place in their product is 5 Which of the following statement(s) is/are correct?

Let two fair six-faced dice A and B be thrown simultaneously. If E_1 is the event that die A shows up four, E_2 is the event that die B shows up two and E_3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true ? (1) E_1 and E_2 are independent. (2) E_2 and E_3 are independent. (3) E_1 and E_3 are independent. (4) E_1 , E_2 and E_3 are independent.

A ship is fitted with three engines E_(1),E_(2),and E_(3) the engines function independently of each othe with respectively probability 1//2,1//4, and 1//4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X_(1),X_(2), and X_(3) denote, respectively, the events that the engines E_(1),E_(2),and E_(3) are functioning. Which of the following is (are) true?

If E and F are independent events such that P(E')=0.2 and P(F')=0.5, find P(EnnF)

Numberse are selected at random, one at a time, from the two-digit numbers 00,01,02,….99 with replacement. An event E occurs if and only if the product of the two digits of a selected number is 18. If four numbers are selected, find probability that the event E occurs at least 3 times.

Of the three independent event E_(1),E_(2) and E_(3) , the probability that only E_(1) occurs is alpha , only E_(2) occurs is beta and only E_(3) occurs is gamma . If the probavvility p that none of events E_(1), E_(2) or E_(3) occurs satisfy the equations (alpha - 2beta)p = alpha beta and (beta - 3 gamma) p = 2 beta gamma . All the given probabilities are assumed to lie in the interval (0, 1). Then, ("probability of occurrence of " E_(1))/("probability of occurrence of " E_(3)) is equal to

Integrate the following with respect to x: (e^(2x)-1)/(e^(x))

An unbiased normal coin is tossed n times. Let E_(1): event that both heads and tails are present in n tosses. E_(2): event that the coin shows up heads at most once. The value of n for which E_(1) and E_(2) are independent is ______.