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Binomial Probability Theorem

In a hurdle r...

Question

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is. What is the probability that he will knock down fewer than 2 hurdles?

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Solution

Let p and q respectively be the probabilities that the player will clear and knock down the hurdle.

Let X be the random variable that represents the number of times the player will knock down the hurdle.

Therefore, by binomial distribution, we obtain

P (X = x) =

P (player knocking down less than 2 hurdles) = P (X < 2)

= P (X = 0) + P (X = 1)

=

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Similar questions

Q. In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is . What is the probability that he will knock down fewer than 2 hurdles?

Q. In a hurdle race, a player has to cross

5

hurdles. The probability that he will clear each hurdle is

\frac{2}{3}

. The probabilty that he will knock down fewer than

2

(a) \frac{32}{243} (b) \frac{80}{243}

(c) \frac{112}{243} (d) \frac{122}{243}

n

independent trials (finite) of a random experiment, let

X

be the number of times an event

A

occurs. If the probability of success of one trial say

p

and we get the probability of failure of event

A

P (¯ A) = 1 - p = q

. The probability of

r

n

trials is denoted by

P (X = r)

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

, known as binomial distribution of random variable

X

. We also have the following result-

(i) Probability of getting at least

k

P (X \geq K) = \sum_{r = k}^{n}^{n} C_{r} p^{r} q^{n - r}

(ii) Probability of getting at the most

k

P (X \leq K) = \sum_{r = 0}^{n}^{n} C_{r} p^{r} q^{n - r}

\sum_{r = 0}^{n} =^{n} C_{r} p^{r} q^{n - r} = {(p + q)}^{n} = 1

On the basis of above information answer the following question.

In a hurdle race, a player has to cross

10

hurdles.The probability that he will cross each hurdle is

\frac{5}{6}

, then the probability that he will knock down fewer than two hurdle is

Q. In a hurdle race, a runner has probability

p

of jumping over a specific hurdle. Given that in

5

trials, the runner succeeded

3

times, the conditional probability that the runner had succeeded in the first trail is

Q. In a hurdle race, a runner has probability

p

of jumping over a specific hurdle. Given that in

5

trials, the rummer succeeded

3

times, the conditional probability that the runner had succeeded in the first trial is

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