Question

calculate the probability of 3 success from a total of 10 independent trials, where the probability of success on each trail is 0.3.​

Answer 1

Answer:

p(e)+p=1

0.3+p=1

p=1-0.3

p=0.7

Answer 2

The required probability = 0.27

Given :

• There are total of 10 independent trials

• The probability of success on each trail is 0.3

To find :

The probability of 3 success

Concept :

If a trial is repeated n times and p is the probability of a success and q that of failure then the probability of r successes is

$\displaystyle \sf{ \sf{P(X=r) = \: \: }\large{ {}^{n} C_r}\: {p}^{r} \: \: {q}^{n - r} } \: \: \: \: \: where \: q \: = 1 - p$

Solution :

Step 1 of 2 :

Write down the number of trials and probability of success

Here it is given that there are total of 10 independent trials

The probability of success on each trail is 0.3

Number of trials = n = 10

Probability of success = p = 0.3

q = 1 - p = 1 - 0.3 = 0.7

Step 2 of 2 :

Find the required probability

The probability of 3 success

$\displaystyle \sf = P(X=3) \:$

$\displaystyle \sf{ {}^{10} C_3\: {p}^{3} \: \: {q}^{10 - 3} } \: \:$

$\displaystyle \sf{ = \large{ {}^{10} C_3}\: { ( 0.3 )}^{3} \: \: { (0.7)}^{7} } \: \:$

$\displaystyle \sf{ = \frac{10 \:! }{3\: ! \: \times \: 7 \:! } \: \: { (0.3 )}^{3} \: \: { (0.7 )}^{7} } \: \:$

$\displaystyle \sf{ = 120 \times 0.027 \times 0.082 }$

$\displaystyle \sf{ = 0.26568 }$

$\displaystyle \sf{ \approx \: 0.27 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ Two dice are thrown together what is the probability number 1 does not appear on both

https://brainly.in/question/6749741

2. probability of a 10 year flood occurring at least once in the next 5 years is

https://brainly.in/question/23287014

3. Find the probability of getting 5 exactly twice in 7 throws of a dice

https://brainly.in/question/3632654

#SPJ3