About 75% of the girls in grade 7 at Grande Rock Middle School prefer colored jeans to the regular blue ones. The randomly generated numbers in the table simulate this situation. The letter C represents colored jeans, and B represents blue jeans.
CCCBC BBCCC CCBBC CCBBC
CCCCC CCCCC BCCCC CBCCC
CCCCB CCCCC BBCCC CCCBB
CCCCC CBCCC BCCBC CCCBB
BCCCC CCCCB CCCBC CCBCC
Based on the data, the estimated probability that exactly four out of five girls prefer colored jeans is
.
well, count up the ones with 4 C's and divide by the total number.
Thank you Steve
To find the estimated probability that exactly four out of five girls prefer colored jeans, we need to count the number of occurrences where exactly four C's (colored jeans) appear in each row.
In the given table, let's count the occurrences:
CCCBC - Exactly four C's
BBCCC - Exactly three C's
CCBBC - Exactly four C's
CCBBC - Exactly four C's
CCCCC - Exactly five C's
CCCCC - Exactly five C's
BCCCC - Exactly four C's
CCCCB - Exactly four C's
CCCCC - Exactly five C's
CBCCC - Exactly four C's
CCCCC - Exactly five C's
BBCCC - Exactly three C's
CCCBB - Exactly four C's
CCCCC - Exactly five C's
CBCCC - Exactly four C's
BCCBC - Exactly three C's
CCCBB - Exactly four C's
Out of the 16 rows, we have 11 rows where exactly four out of five girls prefer colored jeans.
Therefore, the estimated probability that exactly four out of five girls prefer colored jeans is 11/16 or approximately 0.6875.
To determine the estimated probability that exactly four out of five girls prefer colored jeans, we need to analyze the given data.
Total number of girls in each row = 5
Total number of rows = 5
We will calculate the probability for each row and then sum up the probabilities.
For the first row: CCCBC
There is only one girl who prefers blue jeans, so the probability would be (1/5) * (4/5) * (4/5) * (4/5) = 64/625
Similarly, we can calculate the probabilities for the other rows:
Row 2: BCCCC → (4/5) * (4/5) * (4/5) * (4/5) = 256/625
Row 3: CCCCC → (1/5) * (1/5) * (1/5) * (1/5) = 1/625
Row 4: CCCCC → (1/5) * (4/5) * (4/5) * (1/5) = 16/625
Row 5: BCCCC → (4/5) * (4/5) * (4/5) * (4/5) = 256/625
Now, sum up the probabilities for all the rows:
64/625 + 256/625 + 1/625 + 16/625 + 256/625 = 593/625
Therefore, the estimated probability that exactly four out of five girls prefer colored jeans is 593/625.