WEBVTT
00:00:01.220 --> 00:00:10.140
In a binomial experiment, the probability of success in each trial is 0.3 and 20 trials are performed.
00:00:10.940 --> 00:00:14.740
What is the expected number of successful trials?
00:00:15.670 --> 00:00:20.970
Letβs begin by recalling the two key properties of a binomial experiment.
00:00:21.770 --> 00:00:27.250
A binomial experiment consists of π independent repeated trials.
00:00:27.860 --> 00:00:32.670
There are two possible outcomes to each trial: success and failure.
00:00:33.870 --> 00:00:40.470
This means that any binomial experiment has two key values, denoted by π and π.
00:00:41.580 --> 00:00:47.700
π is the number of trials and π is the probability of success.
00:00:48.560 --> 00:00:55.450
In this question, weβre told that there are 20 trials and the probability of success is 0.3.
00:00:55.910 --> 00:01:01.150
Therefore, π equals 20 and π equals 0.3.
00:01:02.350 --> 00:01:09.420
The expected value or mean denoted by πΈ of π₯ is equal to π multiplied by π.
00:01:10.600 --> 00:01:15.190
In this question, we need to multiply 20 by 0.3.
00:01:16.070 --> 00:01:19.680
0.3 multiplied by 10 is equal to three.
00:01:20.040 --> 00:01:23.150
And multiplying this by two gives us six.
00:01:24.160 --> 00:01:34.700
The expected number of successful trials in an experiment with 20 trials and probability of success of 0.3 is six.
00:01:35.650 --> 00:01:39.440
We know that 0.3 is equal to 30 percent.
00:01:40.200 --> 00:01:44.750
This means we would expect a successful outcome 30 percent of the time.
00:01:45.230 --> 00:01:48.630
We could calculate 30 percent of 20.
00:01:49.260 --> 00:01:54.310
One way of doing this is to find 10 percent and multiply the answer by three.
00:01:55.040 --> 00:01:58.460
Either way, our final answer is six.