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Math  /  Data & Statistics

QuestionNeed Help? Read It Watch it Submit Answer 13. [4/5 Points] DETAILS MY NOTES BBUNDERSTAT12HS 5.R.019. PREVIOUS
An experiment consists of tossing an unfair coin. ( 40%40 \% chance of landing on heads) a specified number of times and recording the outcomes. (a) What is the pabability that the first head will occur on the second trial? (Use 4 decimal places.)

Studdy Solution

STEP 1

1. The probability of landing on heads in a single trial is 0.40 0.40 .
2. The probability of landing on tails in a single trial is 1−0.40=0.60 1 - 0.40 = 0.60 .
3. We are looking for the probability that the first head occurs on the second trial.

STEP 2

1. Identify the sequence of outcomes needed for the first head to occur on the second trial.
2. Calculate the probability of this sequence of outcomes.

STEP 3

To have the first head occur on the second trial, the first trial must be tails, and the second trial must be heads. The sequence of outcomes is: Tails, Heads.

STEP 4

Calculate the probability of the sequence "Tails, Heads":
The probability of tails on the first trial is 0.60 0.60 .
The probability of heads on the second trial is 0.40 0.40 .
The probability of the sequence "Tails, Heads" is:
P(Tails, Heads)=P(Tails)×P(Heads)=0.60×0.40=0.24 P(\text{Tails, Heads}) = P(\text{Tails}) \times P(\text{Heads}) = 0.60 \times 0.40 = 0.24
The probability that the first head will occur on the second trial is:
0.2400 \boxed{0.2400}

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