Three
cards
are
drawn
from
five
cards
lettered
FGHIJ
one
after
the
other
without
replacement
what
is
the
probability
that
the
cards
spell
the
word
FIG
There are 5P3 ways to draw the cards. Only one will spell FIG.
So P(FIG) = 1/60
To find the probability that the cards spell the word "FIG" when drawn one after the other without replacement, we need to calculate the number of favorable outcomes (number of ways we can spell "FIG") and divide it by the total number of possible outcomes.
Favorable Outcomes:
The letters "F", "I", and "G" must be drawn in that order. We have 5 choices for the first card, then 4 choices for the second card, and 3 choices for the third card, since we are drawing without replacement. Therefore, the number of favorable outcomes is 5 * 4 * 3 = 60.
Total Possible Outcomes:
We have 5 choices for the first card, then 4 choices for the second card, and 3 choices for the third card, since we are drawing without replacement. Therefore, the total number of possible outcomes is 5 * 4 * 3 = 60.
Probability:
The probability of drawing the cards that spell "FIG" is the number of favorable outcomes divided by the total number of possible outcomes:
Probability = Favorable Outcomes / Total Possible Outcomes = 60 / 60 = 1.
Therefore, the probability that the cards spell the word "FIG" is 1 or 100%.
To calculate the probability of drawing the cards that spell the word "FIG" from a set of five cards (lettered FGHIJ) drawn one after the other without replacement, we need to determine the number of favorable outcomes (drawing the cards in the correct order) and the total number of possible outcomes.
Step 1: Determine the total number of possible outcomes.
Since there are five cards and we are drawing three cards one after the other without replacement, the total number of possible outcomes can be calculated as follows:
- For the first card, there are five options.
- For the second card, after the first card is drawn, there are only four remaining options.
- For the third card, after the first two cards are drawn, there are only three remaining options.
Hence, the total number of possible outcomes is calculated as: 5 * 4 * 3 = 60.
Step 2: Determine the number of favorable outcomes.
To spell the word "FIG," we must draw the cards in the order F, I, G. Therefore, there is only one favorable outcome.
Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 1 / 60
Probability = 0.0167 or 1.67%
Therefore, the probability that the three cards drawn spell the word "FIG" is 1.67%.