Q. 275.0( 1 Vote )

# Five dice are thrown simultaneously. If the occurrence of 3, 4 or 5 in a single die is considered a success, find the probability of at least 3 successes.

Answer :

Let p denote the probability of getting 3, 4 or 5 in a throw of dice.

Let us find out the value of p.

We know, a dice has 6 faces numbered 1, 2, 3, 4, 5 and 6.

So, the probability of getting a 3, 4 or 5 is given as,

If p denotes the probability of getting success, then let q denote the probability of not getting success.

We can say,

p + q = 1

⇒ q = 1 – p

Let X denote the number of successes in the throw of five dice simultaneously.

Let there be total n number of throws of five dice simultaneously.

Then, the probability of getting r successes out of n throws of dice is given by,

P (X = r) = ^{n}C_{r}p^{r}q^{n-r}

Now, substitute the value of p and q in the above equation.

Also, put n = 5 (Since there are 5 dice throw)

Now, the probability of getting at least 3 successes is given by

Probability of getting at least 3 successes = P(X = 3) + P(X = 4) + P(X = 5)

Thus,

Thus, the probability of getting 3 successes is 1/2.

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A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?

Mathematics - ExemplarState True or False for the statements in the Exercise.

If A, B and C are three independent events such that P(A) = P(B) = P(C) = p, then

P (At least two of A, B, C occur) = 3p^{2} – 2p^{3}

A random variable X has the following probability distribution:

Determine:

(i) K (ii) P (X < 3)

(iii) P (X > 6) (iv) P (0 < X < 3)

**OR**

Find the probability of throwing at most 2 sixes in 6 throws of a single die

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